{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic growth models of SARS-CoV-2 lineage proportions\n",
    "\n",
    "This notebook explores logistic growth models, with the goal of inferring the differential growth rates of different SARS-CoV-2 lineages over time. Before this tutorial you may want to familiarize yourself with [Pyro modeling basics](http://pyro.ai/examples/intro_long.html) and [tensor shapes](http://pyro.ai/examples/tensor_shapes.html) in Pyro and PyTorch.\n",
    "\n",
    "**WARNING**: The purpose of this tutorial is to demonstrate Pyro's modeling and inference syntax. \n",
    "Making reliable inferences about SARS-CoV-2 **is not** the purpose of this tutorial.\n",
    "\n",
    "#### Table of contents\n",
    "\n",
    "* [Overview](#Overview)\n",
    "* [Loading data](#Loading-data)\n",
    "* [A First Model](#A-first-model)\n",
    "* [A regional model](#A-regional-model)\n",
    "* [An alternative regional model](#An-alternative-regional-model)\n",
    "* [Generalizations](#Generalizations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview <a name=\"Overview\" />\n",
    "\n",
    "When different strains/lineages/variants of a virus like SARS-CoV-2 circulate in a population, those lineages that have the largest fitness will tend to dominate, and those lineages that are least fit will tend to be outcompeted by the fittest lineages.\n",
    "In this tutorial we set out to infer (differential) growth rates for different \n",
    "SARS-CoV-2 lineages using a spatio-temporal dataset of SARS-CoV-2 genetic sequences.\n",
    "We'll start with the simplest possible model and then move on to more complex models with hierarchical structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using CPU\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import datetime\n",
    "from functools import partial\n",
    "import numpy as np\n",
    "import torch\n",
    "import pyro\n",
    "import pyro.distributions as dist\n",
    "from pyro.infer import SVI, Trace_ELBO\n",
    "from pyro.infer.autoguide import AutoNormal\n",
    "from pyro.optim import ClippedAdam\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "if torch.cuda.is_available():\n",
    "    print(\"Using GPU\")\n",
    "    torch.set_default_device(\"cuda\")\n",
    "else:\n",
    "    print(\"Using CPU\")\n",
    "\n",
    "smoke_test = ('CI' in os.environ)  # for use in continuous integration testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading data <a name=\"Loading-data\" />\n",
    "\n",
    "Our data consist of a few million genetic sequences of SARS-CoV-2 viruses, clustered into [PANGO lineages](https://cov-lineages.org), and aggregated into a few hundred regions globally and into 28-day time bins. Preprocessing was performed by Nextstrain's [ncov](https://docs.nextstrain.org/projects/ncov/en/latest/reference/remote_inputs.html) tool, and aggregation was performed by the Broad Institute's [pyro-cov](https://github.com/broadinstitute/pyro-cov/blob/master/scripts/preprocess_nextstrain.py) tool."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts: Tensor of shape (27, 202, 1316) on cpu\n",
      "features: Tensor of shape (1316, 2634) on cpu\n",
      "lineages: list of length 1316\n",
      "locations: list of length 202\n",
      "mutations: list of length 2634\n",
      "sparse_counts.index: Tensor of shape (3, 57129) on cpu\n",
      "sparse_counts.total: Tensor of shape (27, 202) on cpu\n",
      "sparse_counts.value: Tensor of shape (57129,) on cpu\n",
      "start_date: datetime\n",
      "time_step_days: int\n"
     ]
    }
   ],
   "source": [
    "from pyro.contrib.examples.nextstrain import load_nextstrain_counts\n",
    "dataset = load_nextstrain_counts()\n",
    "\n",
    "def summarize(x, name=\"\"):\n",
    "    if isinstance(x, dict):\n",
    "        for k, v in sorted(x.items()):\n",
    "            summarize(v, name + \".\" + k if name else k)\n",
    "    elif isinstance(x, torch.Tensor):\n",
    "        print(f\"{name}: {type(x).__name__} of shape {tuple(x.shape)} on {x.device}\")\n",
    "    elif isinstance(x, list):\n",
    "        print(f\"{name}: {type(x).__name__} of length {len(x)}\")\n",
    "    else:\n",
    "        print(f\"{name}: {type(x).__name__}\")\n",
    "summarize(dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial our interest is in the 3-dimensional tensor\n",
    "of counts `dataset[\"counts\"]`, which has shape (T, R, L) where `T` is the number of time bins, `R` is the number of regions, and `L` is the number of strains or PANGO lineages, and `dataset[\"counts\"][t,r,l]` is the number of samples in the corresponding time-region-location bin.\n",
    "The count data are heavily skewed towards a few large regions and dominant lineages like `B.1.1.7` and `B.1.617.2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(8, 3), sharey=True)\n",
    "for i, name in enumerate([\"time bin\", \"location\", \"lineage\"]):\n",
    "    counts = dataset[\"counts\"].sum(list({0, 1, 2} - {i}))\n",
    "    Y = counts.sort(0, True).values\n",
    "    axes[i].plot(Y)\n",
    "    axes[i].set_xlim(0, None)\n",
    "    axes[0].set_ylim(1, None)\n",
    "    axes[i].set_yscale(\"log\")\n",
    "    axes[i].set_xlabel(f\"rank\", fontsize=18)\n",
    "    axes[i].set_title(f\"{len(Y)} {name}s\")\n",
    "axes[0].set_ylabel(\"# samples\", fontsize=18)\n",
    "plt.subplots_adjust(wspace=0.05);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helpers for manipulating data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_lineage_id(s):\n",
    "    \"\"\"Get lineage id from string name\"\"\"\n",
    "    return np.argmax(np.array([s]) == dataset['lineages'])\n",
    "\n",
    "def get_location_id(s):\n",
    "    \"\"\"Get location id from string name\"\"\"\n",
    "    return np.argmax(np.array([s]) == dataset['locations'])\n",
    "\n",
    "def get_aggregated_counts_from_locations(locations):\n",
    "    \"\"\"Get aggregated counts from a list of locations\"\"\"\n",
    "    return sum([dataset['counts'][:, get_location_id(loc)] for loc in locations])\n",
    "\n",
    "start = dataset[\"start_date\"]\n",
    "step = datetime.timedelta(days=dataset[\"time_step_days\"])\n",
    "date_range = np.array([start + step * t for t in range(len(dataset[\"counts\"]))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A first model <a name=\"A-first-model\" />\n",
    "\n",
    "First let's zoom-in on Massachusetts and a few surrounding states:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "northeast_states = ['USA / Massachusetts', \n",
    "                    'USA / New York', \n",
    "                    'USA / Connecticut', \n",
    "                    'USA / New Hampshire',\n",
    "                    'USA / Vermont',\n",
    "                    'USA / New Jersey',\n",
    "                    'USA / Maine',\n",
    "                    'USA / Rhode Island', \n",
    "                    'USA / Pennsylvania']\n",
    "\n",
    "northeast_counts = get_aggregated_counts_from_locations(northeast_states)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next let's extract sublineages corresponding to two of the [WHO variants of concern](https://www.who.int/en/activities/tracking-SARS-CoV-2-variants/), Alpha and Delta:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The Alpha and Delta variants include many PANGO lineages, which we need to aggregate.\n",
    "Q_lineages = [lin for lin in dataset['lineages'] if lin[:2] == 'Q.']\n",
    "AY_lineages = [lin for lin in dataset['lineages'] if lin[:3] == 'AY.']\n",
    "\n",
    "alpha_lineages = ['B.1.1.7'] + Q_lineages\n",
    "delta_lineages = ['B.1.617.2'] + AY_lineages\n",
    "\n",
    "alpha_ids = [get_lineage_id(lin) for lin in alpha_lineages]\n",
    "delta_ids = [get_lineage_id(lin) for lin in delta_lineages]\n",
    "\n",
    "alpha_counts = northeast_counts[:, alpha_ids].sum(-1)\n",
    "delta_counts = northeast_counts[:, delta_ids].sum(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([27, 2])\n"
     ]
    }
   ],
   "source": [
    "# Let's combine the counts into a single tensor\n",
    "alpha_delta_counts = torch.stack([alpha_counts, delta_counts]).T\n",
    "print(alpha_delta_counts.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next let's plot the time series of count proportions (Alpha vs. Delta):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We skip the first year or so of the pandemic when Alpha and Delta are not present\n",
    "start_time = 13\n",
    "total_counts = (alpha_counts + delta_counts)[start_time:]\n",
    "dates = date_range[start_time:]\n",
    "plt.figure(figsize=(7, 4))\n",
    "plt.plot(dates, alpha_counts[start_time:] / total_counts, \n",
    "         label='Alpha')\n",
    "plt.plot(dates, delta_counts[start_time:] / total_counts, \n",
    "         label='Delta')\n",
    "plt.xlim(min(dates), max(dates))\n",
    "plt.ylabel(\"Proportion\", fontsize=18)\n",
    "plt.xticks(rotation=90)\n",
    "plt.gca().xaxis.set_major_locator(mpl.dates.MonthLocator())\n",
    "plt.gca().xaxis.set_major_formatter(mpl.dates.DateFormatter(\"%b %Y\"))\n",
    "plt.legend(fontsize=18)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that at first Alpha was dominant, but then Delta started outcompeting it until Delta became dominant.\n",
    "\n",
    "### Model definition\n",
    "\n",
    "Instead of attempting to model how the total number of observed sequences varies as a function of time (which depends on complex human behavior), we instead model the *proportion* of sequences at each time step that are Alpha versus Delta. In other words if we observed 8 Alpha lineages and 2 Delta lineages at a given time step, we model the proportions 80% and 20% instead of the raw counts 8 and 2. To do this we use a [Logistic Growth](https://en.wikipedia.org/wiki/Logistic_function) model with a [Multinomial](https://pytorch.org/docs/stable/distributions.html#multinomial) distribution as the likelihood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def basic_model(counts):\n",
    "    T, L = counts.shape\n",
    "\n",
    "    # Define plates over lineage and time\n",
    "    lineage_plate = pyro.plate(\"lineages\", L, dim=-1)\n",
    "    time_plate = pyro.plate(\"time\", T, dim=-2)\n",
    "\n",
    "    # Define a growth rate (i.e. slope) and an init (i.e. intercept) for each lineage\n",
    "    with lineage_plate:\n",
    "        rate = pyro.sample(\"rate\", dist.Normal(0, 1))\n",
    "        init = pyro.sample(\"init\", dist.Normal(0, 1))\n",
    "\n",
    "    # We measure time in units of the SARS-CoV-2 generation time of 5.5 days\n",
    "    time = torch.arange(float(T)) * dataset[\"time_step_days\"] / 5.5\n",
    "    \n",
    "    # Assume lineages grow linearly in logit space\n",
    "    logits = init + rate * time[:, None]\n",
    "    \n",
    "    # We use the softmax function (the multivariate generalization of the \n",
    "    # sigmoid function) to define normalized probabilities from the logits\n",
    "    probs = torch.softmax(logits, dim=-1)\n",
    "    assert probs.shape == (T, L)\n",
    "    \n",
    "    # Observe counts via a multinomial likelihood.\n",
    "    with time_plate:\n",
    "        pyro.sample(\n",
    "            \"obs\",\n",
    "            dist.Multinomial(probs=probs.unsqueeze(-2), validate_args=False),\n",
    "            obs=counts.unsqueeze(-2),\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the graphical structure of our model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: %3 Pages: 1 -->\n",
       "<svg width=\"166pt\" height=\"182pt\"\n",
       " viewBox=\"0.00 0.00 166.00 182.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 178)\">\n",
       "<title>%3</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-178 162,-178 162,4 -4,4\"/>\n",
       "<g id=\"clust1\" class=\"cluster\">\n",
       "<title>cluster_lineages</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8,-91 8,-166 150,-166 150,-91 8,-91\"/>\n",
       "<text text-anchor=\"middle\" x=\"119\" y=\"-98.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">lineages</text>\n",
       "</g>\n",
       "<g id=\"clust2\" class=\"cluster\">\n",
       "<title>cluster_time</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"44,-8 44,-83 114,-83 114,-8 44,-8\"/>\n",
       "<text text-anchor=\"middle\" x=\"93.5\" y=\"-15.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">time</text>\n",
       "</g>\n",
       "<!-- rate -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>rate</title>\n",
       "<ellipse fill=\"#ffffff\" stroke=\"#000000\" cx=\"115\" cy=\"-140\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"115\" y=\"-136.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">rate</text>\n",
       "</g>\n",
       "<!-- obs -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>obs</title>\n",
       "<ellipse fill=\"#c0c0c0\" stroke=\"#000000\" cx=\"79\" cy=\"-57\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"79\" y=\"-53.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">obs</text>\n",
       "</g>\n",
       "<!-- rate&#45;&gt;obs -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>rate&#45;&gt;obs</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M107.3653,-122.3978C102.4641,-111.0977 96.0074,-96.2116 90.4926,-83.4967\"/>\n",
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       "</g>\n",
       "<!-- init -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>init</title>\n",
       "<ellipse fill=\"#ffffff\" stroke=\"#000000\" cx=\"43\" cy=\"-140\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"43\" y=\"-136.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">init</text>\n",
       "</g>\n",
       "<!-- init&#45;&gt;obs -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>init&#45;&gt;obs</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M50.6347,-122.3978C55.5359,-111.0977 61.9926,-96.2116 67.5074,-83.4967\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"70.7315,-84.8591 71.4998,-74.2922 64.3096,-82.0737 70.7315,-84.8591\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x7fc7d7c400f0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pyro.render_model(partial(basic_model, alpha_delta_counts))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define a helper for fitting models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_svi(model, lr=0.1, num_steps=1001, log_every=250):\n",
    "    pyro.clear_param_store()  # clear parameters from previous runs\n",
    "    pyro.set_rng_seed(20211214)\n",
    "    if smoke_test:\n",
    "        num_steps = 2\n",
    "        \n",
    "    # Define a mean field guide (i.e. variational distribution)\n",
    "    guide = AutoNormal(model, init_scale=0.01)\n",
    "    optim = ClippedAdam({\"lr\": lr, \"lrd\": 0.1 ** (1 / num_steps)})\n",
    "    svi = SVI(model, guide, optim, Trace_ELBO())\n",
    "    \n",
    "    # Train (i.e. do ELBO optimization) for num_steps iterations\n",
    "    losses = []\n",
    "    for step in range(num_steps):\n",
    "        loss = svi.step()\n",
    "        losses.append(loss)\n",
    "        if step % log_every == 0:\n",
    "            print(f\"step {step: >4d} loss = {loss:0.6g}\")\n",
    "            \n",
    "    # Plot to assess convergence.\n",
    "    plt.figure(figsize=(6, 3))\n",
    "    plt.plot(losses)\n",
    "    plt.xlabel(\"SVI step\", fontsize=18)\n",
    "    plt.ylabel(\"ELBO loss\", fontsize=18)\n",
    "    plt.tight_layout()\n",
    "\n",
    "    return guide"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's fit `basic_model` and inspect the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step    0 loss = 103782\n",
      "step  250 loss = 3373.05\n",
      "step  500 loss = 1299.14\n",
      "step  750 loss = 524.81\n",
      "step 1000 loss = 304.319\n",
      "step 1250 loss = 278.005\n",
      "step 1500 loss = 261.731\n",
      "CPU times: user 4.69 s, sys: 29.6 ms, total: 4.72 s\n",
      "Wall time: 4.73 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "# We truncate the data to the period with non-zero counts\n",
    "guide = fit_svi(partial(basic_model, alpha_delta_counts[13:]), num_steps=1501)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's inspect the posterior means of our latent parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rate [-0.27021623  0.27021623]\n",
      "init [ 8.870546 -8.870401]\n"
     ]
    }
   ],
   "source": [
    "for k, v in guide.median().items():\n",
    "    print(k, v.data.cpu().numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected the Delta lineage (corresponding to index `1`) has a differential growth rate advantage with respect to the Alpha lineage (corresponding to index `0`) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiplicative advantage: 1.72\n"
     ]
    }
   ],
   "source": [
    "print(\"Multiplicative advantage: {:.2f}\".format(\n",
    "      np.exp(guide.median()['rate'][1] - guide.median()['rate'][0])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This seems like it might be an overestimate. Can we get better estimates by modeling each spatial region individually?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A regional model <a name=\"A-regional-model\"/>\n",
    "\n",
    "Instead of focusing on northeastern US states we now consider the entire global dataset and do not aggregate across regions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts.shape:  torch.Size([27, 202, 2])\n",
      "number of regions: 202\n"
     ]
    }
   ],
   "source": [
    "# First extract the data we want to use\n",
    "alpha_counts = dataset['counts'][:, :, alpha_ids].sum(-1)\n",
    "delta_counts = dataset['counts'][:, :, delta_ids].sum(-1)\n",
    "counts = torch.stack([alpha_counts, delta_counts], dim=-1)\n",
    "print(\"counts.shape: \", counts.shape)\n",
    "print(f\"number of regions: {counts.size(1)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We skip the first year or so of the pandemic when Alpha and Delta are not present\n",
    "start_time = 13\n",
    "total_counts = (alpha_counts + delta_counts)[start_time:]\n",
    "dates = date_range[start_time:]\n",
    "plt.figure(figsize=(7, 4))\n",
    "plt.plot(dates, delta_counts[start_time:] / total_counts, color=\"C1\", lw=1, alpha=0.5)\n",
    "plt.xlim(min(dates), max(dates))\n",
    "plt.ylabel(\"Proportion\", fontsize=18)\n",
    "plt.xticks(rotation=90)\n",
    "plt.gca().xaxis.set_major_locator(mpl.dates.MonthLocator())\n",
    "plt.gca().xaxis.set_major_formatter(mpl.dates.DateFormatter(\"%b %Y\"))\n",
    "plt.title(f\"Delta/(Alpha+Delta) in {counts.size(1)} regions\", fontsize=18)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Model lineage proportions in each region as multivariate logistic growth\n",
    "def regional_model(counts):\n",
    "    T, R, L = counts.shape\n",
    "        \n",
    "    # Now we also define a region plate in addition to the time/lineage plates\n",
    "    lineage_plate = pyro.plate(\"lineages\", L, dim=-1)\n",
    "    region_plate = pyro.plate(\"region\", R, dim=-2)\n",
    "    time_plate = pyro.plate(\"time\", T, dim=-3)\n",
    "\n",
    "    # We use the same growth rate (i.e. slope) for each region\n",
    "    with lineage_plate:\n",
    "        rate = pyro.sample(\"rate\", dist.Normal(0, 1))\n",
    "        \n",
    "    # We allow the init to vary from region to region\n",
    "    init_scale = pyro.sample(\"init_scale\", dist.LogNormal(0, 2))\n",
    "    with region_plate, lineage_plate:\n",
    "        init = pyro.sample(\"init\", dist.Normal(0, init_scale))\n",
    "\n",
    "    # We measure time in units of the SARS-CoV-2 generation time of 5.5 days\n",
    "    time = torch.arange(float(T)) * dataset[\"time_step_days\"] / 5.5\n",
    "\n",
    "    # Instead of using the softmax function we directly use the \n",
    "    # logits parameterization of the Multinomial distribution\n",
    "    logits = init + rate * time[:, None, None]\n",
    "    \n",
    "    # Observe sequences via a multinomial likelihood.\n",
    "    with time_plate, region_plate:\n",
    "        pyro.sample(\n",
    "            \"obs\",\n",
    "            dist.Multinomial(logits=logits.unsqueeze(-2), validate_args=False),\n",
    "            obs=counts.unsqueeze(-2),\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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       "<!-- Title: %3 Pages: 1 -->\n",
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       "<title>init_scale&#45;&gt;init</title>\n",
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       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x7fc7d804c7b8>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pyro.render_model(partial(regional_model, counts))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step    0 loss = 909278\n",
      "step  250 loss = 509502\n",
      "step  500 loss = 630927\n",
      "step  750 loss = 501493\n",
      "step 1000 loss = 1.04533e+06\n",
      "step 1250 loss = 1.98151e+06\n",
      "step 1500 loss = 328504\n",
      "step 1750 loss = 279016\n",
      "step 2000 loss = 310281\n",
      "step 2250 loss = 217622\n",
      "step 2500 loss = 204381\n",
      "step 2750 loss = 176877\n",
      "step 3000 loss = 152123\n",
      "CPU times: user 17.3 s, sys: 965 ms, total: 18.3 s\n",
      "Wall time: 17.3 s\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "guide = fit_svi(partial(regional_model, counts), num_steps=3001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiplicative advantage: 1.17\n"
     ]
    }
   ],
   "source": [
    "print(\"Multiplicative advantage: {:.2f}\".format(\n",
    "      np.exp(guide.median()['rate'][1] - guide.median()['rate'][0])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice this is a lower estimate than the previous global estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An alternative regional model <a name=\"An-alternative-regional-model\" />\n",
    "\n",
    "The regional model we defined above assumed that the `rate` for each lineage did not vary between regions. Here we add additional hierarchical structure and allow the rate to vary from region to region."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regional_model2(counts):\n",
    "    T, R, L = counts.shape\n",
    "    \n",
    "    lineage_plate = pyro.plate(\"lineages\", L, dim=-1)\n",
    "    region_plate = pyro.plate(\"region\", R, dim=-2)\n",
    "    time_plate = pyro.plate(\"time\", T, dim=-3)\n",
    "\n",
    "    # We assume the init can vary a lot from region to region but\n",
    "    # that the rate varies considerably less.\n",
    "    rate_scale = pyro.sample(\"rate_scale\", dist.LogNormal(-4, 2))\n",
    "    init_scale = pyro.sample(\"init_scale\", dist.LogNormal(0, 2))\n",
    "    \n",
    "    # As before each lineage has a latent growth rate\n",
    "    with lineage_plate:\n",
    "        rate_loc = pyro.sample(\"rate_loc\", dist.Normal(0, 1))\n",
    "        \n",
    "    # We allow the rate and init to vary from region to region\n",
    "    with region_plate, lineage_plate:\n",
    "        # The per-region per-lineage rate is governed by a hierarchical prior\n",
    "        rate = pyro.sample(\"rate\",  dist.Normal(rate_loc, rate_scale))\n",
    "        init = pyro.sample(\"init\", dist.Normal(0, init_scale))\n",
    "\n",
    "    # We measure time in units of the SARS-CoV-2 generation time of 5.5 days\n",
    "    time = torch.arange(float(T)) * dataset[\"time_step_days\"] / 5.5\n",
    "    logits = init + rate * time[:, None, None]\n",
    "    \n",
    "    # Observe sequences via a multinomial likelihood.\n",
    "    with time_plate, region_plate:\n",
    "        pyro.sample(\n",
    "            \"obs\",\n",
    "            dist.Multinomial(logits=logits.unsqueeze(-2), validate_args=False),\n",
    "            obs=counts.unsqueeze(-2),\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pyro.render_model(partial(regional_model2, counts))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step    0 loss = 2.14938e+06\n",
      "step  250 loss = 1.44698e+06\n",
      "step  500 loss = 1.24936e+06\n",
      "step  750 loss = 701128\n",
      "step 1000 loss = 602609\n",
      "step 1250 loss = 530833\n",
      "step 1500 loss = 454014\n",
      "step 1750 loss = 450981\n",
      "step 2000 loss = 384790\n",
      "step 2250 loss = 340659\n",
      "step 2500 loss = 305373\n",
      "step 2750 loss = 279524\n",
      "step 3000 loss = 262679\n",
      "CPU times: user 25 s, sys: 1.05 s, total: 26 s\n",
      "Wall time: 25.1 s\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "guide = fit_svi(partial(regional_model2, counts), num_steps=3001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiplicative advantage: 1.14\n"
     ]
    }
   ],
   "source": [
    "print(\"Multiplicative advantage: {:.2f}\".format(\n",
    "      (guide.median()['rate_loc'][1] - guide.median()['rate_loc'][0]).exp()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generalizations <a name=\"Generalizations\" />\n",
    "\n",
    "So far we've seen how to model two variants at a time either globally or split across multiple regions, and how to use [pyro.plate](https://docs.pyro.ai/en/stable/primitives.html#pyro.primitives.plate) to model multiple variants or regions or times.\n",
    "\n",
    "What other models can you think of that might make epidemiological sense? Here are some ideas:\n",
    "\n",
    "- Can you create a model over more than two variants, or even over all PANGO lineages?\n",
    "- What variables should be shared across lineages, across regions, or over time?\n",
    "- How might you deal with changes of behavior over time, e.g. pandemic waves or vaccination?\n",
    "\n",
    "For an example of a larger Pyro model using SARS-CoV-2 lineage data like this, see our paper \"Analysis of 2.1 million SARS-CoV-2 genomes identifies mutations associated with transmissibility\" ([preprint](https://www.medrxiv.org/content/10.1101/2021.09.07.21263228v1) | [code](https://github.com/broadinstitute/pyro-cov)), and also the [Bayesian workflow tutuorial](workflow.html) using a slightly smaller dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
